basic_quantities.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<div style=\"display: flex; align-items: center;\">\n",
    "    <img src=\"https://github.com/nagelt/Teaching_Scripts/raw/9d9e29ecca4b04eaf7397938eacbf116d37ddc93/Images/TUBAF_Logo_blau.png\" width=\"500\" height=\"auto\" height=\"auto\" style=\"margin-right: 100px;\" />\n",
    "    <div>\n",
    "        <p><strong>Prof. Dr. Thomas Nagel</strong></p>\n",
    "        <p>Chair of Soil Mechanics and Foundation Engineering<br>Geotechnical Institute<br>Technische Universität Bergakademie Freiberg.</p>\n",
    "        <p><a href=\"https://tu-freiberg.de/en/soilmechanics\">https://tu-freiberg.de/en/soilmechanics</a></p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Illustration grundlegender Kennwerte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import widgets\n",
    "from ipywidgets import interact\n",
    "import matplotlib.cm as cm\n",
    "\n",
    "#Some plot settings\n",
    "import plot_functions.plot_settings\n",
    "%run plot_functions/basic_quantities_plots.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porosität (Porenanteil) $n$ und Feststoffanteil $n_\\text{s}$ sind wie folgt verknüpft:\n",
    "\n",
    "$$\n",
    "    n = \\phi = \\frac{V_\\text{p}}{V} = \\frac{V - V_\\text{s}}{V} = 1 - n_\\text{s} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Porenzahl $e$ ergibt sich entsprechend zu\n",
    "\n",
    "$$\n",
    "    e = \\frac{V_\\text{p}}{V_\\text{s}} = \\frac{V - V_\\text{s}}{V_\\text{s}} = \\frac{1}{1 - n} - 1 = \\frac{n}{1-n}\n",
    "$$\n",
    "\n",
    "Die folgende Abbildung verdeutlicht die resultierenden nichtlinearen Zusammenhänge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "def porenzahl(porosity):\n",
    "    return porosity/(1.-porosity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.3, description='$n$', max=0.95, step=0.05), Output()), _dom_classes=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#HIDDEN\n",
    "@interact(por=widgets.FloatSlider(min=0.0, max=0.95, step=0.05, value=0.3,\n",
    "    description=r'$n$'))\n",
    "def plot_slide(por = 0.3):\n",
    "    plot_e_n(por)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Porosität ist im gesamten Bereich von reinem Festkörper ($n = 0$) bis zum reinen Fluid ($n = 1$) definiert. Die Porenzahl verschwindet für den reinen Feststoff, $e=0$, wird aber für das reine Fluid unendlich."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es sei nun zusätzlich die Masse des feuchten Bodens $m$ gegeben. Daraus lassen sich wiederum Größen wie Wassergehalt $w$ und Sättigung $S_\\text{r}$ bestimmen:\n",
    "\n",
    "$$\n",
    "    w = \\frac{m_\\text{w}}{m_\\text{d}} = \\frac{m-m_\\text{d}}{m_\\text{d}}\n",
    "$$\n",
    "sowie\n",
    "$$\n",
    "    S = \\frac{V_\\text{w}}{V_\\text{p}} = \\frac{V_\\text{w}}{V}\\frac{V}{V_\\text{p}} = \\frac{n_\\text{w}}{n}\n",
    "$$\n",
    "\n",
    "Eine Umrechnung der Massen in Volumina erfolgt mittels der Wasserdichte $\\varrho_\\text{w} = 1000\\,$kg$\\,$m$^{-3}$ und liefert\n",
    "\n",
    "$$\n",
    "    V_\\text{w} = \\frac{m_\\text{w}}{\\varrho_\\text{w}}\n",
    "$$\n",
    "\n",
    "Somit können wir schreiben:\n",
    "$$\n",
    "    S = \\frac{(m - m_\\text{d})}{\\varrho_\\text{w} e V_\\text{s}} = \\frac{(m - m_\\text{d})\\varrho_\\text{s}}{\\varrho_\\text{w} e m_\\text{d}} = \\frac{\\varrho_\\text{s}}{\\varrho_\\text{w}}\\frac{w}{e}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "def saturation(w,e):\n",
    "    rho_s = 2600. #kg/m³ unterstellte Korndichte\n",
    "    rho_w = 1000. #kg/m³ Wasserdichte\n",
    "    return rho_SR/rho_WR * w/e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "interactive(children=(FloatSlider(value=0.3, description='$n$', max=0.9, min=0.1, step=0.05), FloatSlider(valu…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#HIDDEN\n",
    "@interact(por=widgets.FloatSlider(min=0.1, max=0.9, step=0.05, value=0.3,\n",
    "    description=r'$n$'),\n",
    "         Sat=widgets.FloatSlider(min=0.0, max=1.0, step=0.05, value=0.3,\n",
    "    description=r'$S$'))\n",
    "\n",
    "def plot_slide(por = 0.3, Sat = 0.8):\n",
    "    plot_w_S_n(por,Sat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rechenaufgabe\n",
    "\n",
    "Von einem feuchten grobkörnigen Boden wurde der Porenanteil mit einem Wert von $n=0.3$ und die Wichte mit dem Wert $\\gamma = 19.61\\,\\text{kN}\\,\\text{m}^{-3}$ ermittelt.\n",
    "\n",
    "Wie hoch ist der Wassergehalt dieses Bodens, wenn\n",
    "\n",
    "    a) seine Korndichte 2700 kg/m³ beträgt bzw.\n",
    "    b) zum Erreichen des gesättigten Zustands die Zugabe von 189 Liter Wasser pro m³ erforderlich ist?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "n = 0.3\n",
    "gamma = 19.61 # kN/m³\n",
    "rho_s = 2700. # kg/m³\n",
    "Delta_n_W = 0.189 #Änderung des Porenwasseranteils m³/m³"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Wassergehalt ist mit \n",
    "\n",
    "$$\n",
    "    w = \\frac{m_\\text{w}}{m_\\text{d}} = \\frac{m}{m_\\text{d}} - 1\n",
    "$$\n",
    "\n",
    "gegeben.\n",
    "\n",
    "### Teilaufgabe a)\n",
    "\n",
    "Die Feucht und Trockenmassen des Bodens folgen aus\n",
    "\n",
    "\\begin{align}\n",
    "    m &= \\varrho V = \\frac{\\gamma}{g} V\n",
    "    \\\n",
    "    m_\\text{d} &= \\varrho_\\text{d} V = \\varrho_\\text{s} V_\\text{s}\n",
    "    \\\n",
    "    &= (1-n) \\varrho_\\text{s} V\n",
    "\\end{align}\n",
    "\n",
    "Somit können wir für den Wassergehalt schreiben:\n",
    "\n",
    "$$\n",
    "    w = \\frac{m}{m_\\text{d}} - 1 = \\frac{\\gamma}{g (1-n) \\varrho_\\text{s}} - 1 =  \\frac{\\gamma}{(1-n) \\gamma_\\text{s}} - 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Der Wassergehalt für Teilaufgabe a) beträgt 5.77 Prozent.\n"
     ]
    }
   ],
   "source": [
    "#HIDDEN\n",
    "w = gamma/((1-n)*9.81*rho_s * 1.e-3) - 1\n",
    "print(\"Der Wassergehalt für Teilaufgabe a) beträgt %.2f Prozent.\" %(w*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Teilaufgabe b)\n",
    "\n",
    "Bei Vollsättigung ist der gesamte Porenraum des Bodens mit Wasser gefüllt. Das heißt\n",
    "\n",
    "$$\n",
    "    V_\\text{w2} = V_\\text{p} = n V\n",
    "$$\n",
    "\n",
    "Zuvor ist das Porenvolumen mit Wasser und Luft gefüllt:\n",
    "\n",
    "$$\n",
    "    V_\\text{p} = V_\\text{w1} + V_\\text{a1}\n",
    "$$\n",
    "\n",
    "Die Differenz beider Wasservolumina entspricht der zugegebenen Wassermenge $\\Delta V_\\text{w} = 189\\,$l.\n",
    "\n",
    "$$\n",
    "    V_\\text{w2} - V_\\text{w1} = V_\\text{a1}\n",
    "$$\n",
    "\n",
    "d.h. beim Aufsättigen wird das Porenluftvolumen vom zugegebenen Wasser verdrängt.\n",
    "\n",
    "Damit ergibt sich\n",
    "\n",
    "$$\n",
    "    n V = V_\\text{w1} + \\Delta V_\\text{w}\n",
    "$$\n",
    "\n",
    "Bzw. mit dem Porenwasseranteil $n_\\text{w}$\n",
    "\n",
    "$$\n",
    "    n = n_\\text{w1} + \\Delta n_\\text{w}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Die maximale Wassermenge im Porenraum beträgt 300.00 Liter pro m³ Boden.\n",
      "Im Ausgangszustand enthielt 1 m³ Boden 111.00 Liter Wasser.\n"
     ]
    }
   ],
   "source": [
    "#HIDDEN\n",
    "n_w1 = n - Delta_n_W\n",
    "print(\"Die maximale Wassermenge im Porenraum beträgt %.2f Liter pro m³ Boden.\" %(n*1000.))\n",
    "print(\"Im Ausgangszustand enthielt 1 m³ Boden %.2f Liter Wasser.\" %(n_w1*1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Volumen $V_\\text{w1}$ entspricht der Wassermasse $m_\\text{w1} = \\varrho_\\text{w} V_\\text{w1}$ mit $\\varrho_\\text{w} = 1000\\,$kg/m³.\n",
    "\n",
    "Die Trockenmasse des Bodens ergibt sich zu\n",
    "\n",
    "$$\n",
    "    m_\\text{d} = m - m_\\text{w1} = \\frac{\\gamma}{g} V - \\varrho_\\text{w} V_\\text{w1}\n",
    "$$\n",
    "\n",
    "$$\n",
    "    w = \\frac{m_\\text{w1}}{m_\\text{d}} = \\frac{m_\\text{w1}}{m - m_\\text{w1}} = \\frac{V_\\text{w1} \\varrho_\\text{w}}{\\frac{\\gamma}{g} V - \\varrho_\\text{w} V_\\text{w1}} = \\frac{n_\\text{w1} \\varrho_\\text{w}}{\\frac{\\gamma}{g} - \\varrho_\\text{w} n_\\text{w1}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Der Wassergehalt für Teilaufgabe a) beträgt 5.88 Prozent.\n"
     ]
    }
   ],
   "source": [
    "#HIDDEN\n",
    "rho_w = 1000.\n",
    "w = n_w1 * rho_w / (gamma*1000/9.81 - rho_w * n_w1)\n",
    "print(\"Der Wassergehalt für Teilaufgabe a) beträgt %.2f Prozent.\" %(w*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Einordnung der Lagerungsdichte von Böden nach $D$ und $I_D$\n",
    "\n",
    "Die Einordnung der Lagerungsdichte wird in von Soos und Engel (Grundbau Taschenbuch) in Bezug auf $D$ angegeben. In DIN EN ISO 14688-2, Tabelle 5 jedoch in Bezug auf $I_D$. Die Zahlenwerte der Übergangspunkte unterscheiden sich. Im Folgenden zeigen wir, dass eine 1:1 Korrespondenz nicht besteht.\n",
    "\n",
    "\n",
    "Seien $\\text{max}\\,n = 0.476$ und $\\text{min}\\,n = 0.259$. Dann ergeben sich für die Einteilung nach GBT folgende Porositäten an den Übergängen der Lagerungsdichteeinordnung bezogen auf $D$:\n",
    "\n",
    "- $0 \\leq D < 0.15$: sehr locker\n",
    "- $0.15 < D \\leq 0.3$: locker\n",
    "- $0.3 < D \\leq 0.5$: mitteldicht\n",
    "- $0.5 < D \\leq 0.8$: dicht\n",
    "- $0.8 < D$: sehr dicht"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "D = np.array([0,0.15,0.3,0.5,0.8,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "n_max = 0.476\n",
    "n_min = 0.259\n",
    "\n",
    "e_max = porenzahl(n_max)\n",
    "e_min = porenzahl(n_min)\n",
    "\n",
    "def porosity_from_D(D):\n",
    "    return n_max - D * (n_max - n_min)\n",
    "\n",
    "def I_D(porenzahl):\n",
    "    return (e_max - porenzahl)/(e_max - e_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#HIDDEN\n",
    "n = porosity_from_D(D)\n",
    "e = porenzahl(n)\n",
    "ID = I_D(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lagerungsdichte D = 0.000. Porosität von n = 0.476. Porenzahl e = 0.908. Bezogene Lagerungsdichte I_D = 0.000\n",
      "Lagerungsdichte D = 0.150. Porosität von n = 0.443. Porenzahl e = 0.797. Bezogene Lagerungsdichte I_D = 0.200\n",
      "Lagerungsdichte D = 0.300. Porosität von n = 0.411. Porenzahl e = 0.698. Bezogene Lagerungsdichte I_D = 0.377\n",
      "Lagerungsdichte D = 0.500. Porosität von n = 0.367. Porenzahl e = 0.581. Bezogene Lagerungsdichte I_D = 0.586\n",
      "Lagerungsdichte D = 0.800. Porosität von n = 0.302. Porenzahl e = 0.433. Bezogene Lagerungsdichte I_D = 0.850\n",
      "Lagerungsdichte D = 1.000. Porosität von n = 0.259. Porenzahl e = 0.350. Bezogene Lagerungsdichte I_D = 1.000\n"
     ]
    }
   ],
   "source": [
    "#HIDDEN\n",
    "for i in range(len(D)):\n",
    "    print(\"Lagerungsdichte D = %.3f. Porosität von n = %.3f. Porenzahl e = %.3f. Bezogene Lagerungsdichte I_D = %.3f\" %(D[i],n[i],e[i],ID[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x71d27c18f890>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ds = np.linspace(0,1,100)\n",
    "plt.plot(Ds, I_D(porenzahl(porosity_from_D(Ds))))\n",
    "plt.plot(Ds,Ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}